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Chapter 2: Problem 35

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-1,4), r=2$$

Short Answer

Expert verified
The standard form of the equation of the circle with the given center (-1,4) and radius 2 is \( (x + 1)^2 + (y - 4)^2 = 4 \).

Step by step solution

01

Identify the values of h, k and r

In the given problem, the center of the circle is at the point (-1, 4) and the radius of the circle is 2. So, \( h = -1 \), \( k = 4 \), and \( r = 2 \).
02

Substitute the values into the standard equation

Now, substitute these values into the standard equation of a circle \( (x - h)^2 + (y - k)^2 = r^2 \) to get: \( (x - (-1))^2 + (y - 4)^2 = 2^2 \).
03

Simplify the equation

Simplifying the equation gives: \( (x + 1)^2 + (y - 4)^2 = 4 \). This is the standard form of the equation of the circle with center at point (-1,4) and radius 2.

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